Does a 12" PowerBook have a PRAM battery on the logic board?

We got an 867MHz 12" Aluminum PowerBook in today that doesn't seem to want to hold PRAM values any longer than 5 minutes. It doesn't seem to matter if it's plugged in and using the AC adapter as the source or the battery (as long as it's charged, of course ).
I've gone through the typical battery of tests, like removing the Airport, add-on RAM, etc. but the problems persist. To get the item to boot, I've been repeatedly resetting the PMU (shift-option-command + power button) followed by a PRAM reset (option-command-P-R + power button) and eventually it will chime and start to boot. I suspect that I can end up isolating this to a specific set of steps. One of the oddities I've noticed is that when doing this, the power isn't actually off. For example, if I do the PRAM reset, the item will appear to be dead, but if I hit the caps lock key it's clear that the power is still on.
Once the item boots, I can power it on and off, and it will reboot, as long as I don't let it sit any more than 5 minutes. If I let it sit 5 minutes or more, then I need to go through this whole reset game again.
I've seen stuff like this happen on PCs that often have ROM/PROM batteries installed (sometimes removable, sometimes soldered to the board) that retain system settings. There seems to be something that looks like one of these batteries installed on this motherboard, but none of Apple's tech repair manuals reference replacing it, and it almost looks like its welded to a connector, but then again I'm not sure it's even a battery.
So the question is: Does this motherboard have a PRAM battery on it that's failing? If there is one, is there a replacement or replacement kit available, or am I barking up the wrong tree all together?
Thanks in advance.

From what I can tell, this device uses a "mega capacitor" to maintain the charge on the memory. It looks almost like a battery that I put into one of my old cameras. This capacitor sits between the trackpad and the optical drive. The owner of this system did a DVD upgrade himself and it appears in the process he actually knocked this capacitor off it's base on the mother board. It superficially APPEARS to be connected because there's a bar on the top end of the capacitor soldered to the motherboard that's holding it in place, but the bottom end broke off the motherboard.
The boss of our company theorizes as follows:
1. The PRAM and NVRAM has a high impedance, and when the mega capacitor is properly connected and without power, the discharge rate based on the RC time constant is very long (probably weeks...maybe months).
2. When power is turned off it's the duty of this effective RC network to maintain PRAM and NVRAM since the discharge rate is so slow.
3. With this capacitor busted off, the only capacitance that exists in the circuit is likely that of RF bypass capacitors and any other capacitors that may be used to filter out the supply. Since these are likely much, much lower in value the RC time constant becomes minutes instead of days/weeks/months.
I think this is a good theory for the following reasons:
1. If the unit sits, powered off, for any amount of time greater than 3-4 minutes and it's powered up, the unit comes on, but the CPU doesn't start processing. The optical media initializes, the caps lock key will light, and if you listen closely to the unit you can hear stuff running....but the CPU doesn't start. The conjecture is that the all PRAM/NVRAM parameters have been lost and when the CPU starts it sees nothing there and hence, does nothing. The unit is actually running, it just doesn't do anything.
2. If the unit sits, powered off, for any amount of time greater than 3-4 minutes, the following process will allow it to start up:
a. Turn the power on and leave it on for about 2-3 minutes. This is the dysfunctional state identified above, but what seems to be happening is that the effective RC network is being charged.
b. After several minutes, turn the unit off and then immediately turn it on.
c. The unit boots successfully.
d. We can turn the unit off, and turn it on again, and it will successfully boot as long as we do it relatively quickly (within a minute or two), but if it's left off more than that then the "game" identified in steps a-c must be repeated.
To me this implies the unit relies completely on the "mega-capacitor" to retain voltage on the PRAM/NVRAM. It sort of makes sense because the equivalent impedance of a battery is low compared to that of the RAM chips and it would have the effect of limiting the RC time constant needed for the unit to retain it's PRAM/NVRAM parameters for a very long period of time. That isn't to say the battery isn't supplying anything to the unit when power is off...it may very well be, but I suspect it simply isn't doing it to this circuit.
Does this theory make sense?

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